Doc Brown's secret wealth allowed him to fund his own inventions long before the events of Back to the Future Part I. As smart as he is, Christopher Lloyd's Doc Brown wouldn't be able to figure out time travel without a hefty amount of money. All those years of tinkering with different machines and contraptions of varying quality impact Doc Brown's wallet, and since he's never shown to work a side job, the exact source of Doc Brown's funds isn't made entirely clear in the Back to the Future trilogy.
By 1955, Doc Brown is able to afford a wide variety of clocks, a gigantic speaker, and a modified DeLorean. However, Doc Brown still chooses to make a deal with a group of Libyan terrorists in order to get his hands on some plutonium. This is in part because Doc wants to keep his greatest invention from falling into the wrong hands, but also because his reserves of money may be depleting. Although substantial, his wealth is limited, and he doesn't have many alternatives to recover it once it's gone.
Where Doc Brown's Money Comes From In Back To The Future
The Back to the Future trilogy doesn't delve into the source of Doc Brown's wealth, but when he talks about the flux capacitor in the first movie, he mentions, "It's taken me nearly thirty years and my entire family fortune to realize the vision of that day." This passing comment explains that Doc Brown was born into wealth and suggests that he may never have had to work an actual job. Another source of wealth may have involved insurance fraud, as newspaper clippings show that Doc Brown's mansion conveniently burned down sometime before 1985. And last, Doc started carrying a suitcase with notes from all eras with him in Back to the Future Part II.
Why Doc Brown Lived In A Mansion In 1955
Doc Brown's plans for the flux capacitor were barely starting to take shape by the time Marty McFly visits him in 1955. Doc Brown was already working on inventions like the failed brainwave analyzer, but he still lived in the big, lavish mansion he inherited from his family. Since he wasn't obsessed with time travel yet, Doc Brown may not have started to invest all his money into the time machine, so he may have been more careful with his money back then.
Later on, Doc Brown fixated on time travel and likely burned down his mansion in order to fund his main project. What's for certain is that he sold the surrounding terrain for commercial development, which only increased his funds and allowed him to focus full-time on creating the DeLorean time machine. He kept burning through his money, so he couldn't obtain plutonium through legal or ethical means. Doc Brown didn't care too much about money in the Back to the Future trilogy, but thankfully, it didn't matter too much after he began traveling through time with Clara Clayton and their sons.